The Social Network is, along with The Lives of Others, my favourite film so far of the 21st century. It’s a warts-and-all biopic of Mark Zuckerberg, the computer geek who became the world’s youngest billionaire thanks to his invention of Facebook.

It is director David Fincher’s equivalent to Orson Welles’ Citizen Kane: the story of a capitalist who is awe-inspiring in some ways but tragic in others, enviably clever and driven but also repellently ruthless and treacherous.

The irony is that a man who was able to make billions out of social networking, never understood how to make friends, let alone keep the few he had. Alternative titles might have been Revenge of the Nerd, or Despicable Me.

The picture works on three levels. It is an inspiring story of an ambitious young man sticking to his guns and blowing out of the water anyone who gets in his way. It’s a cautionary tale about the price of such single-mindedness. And it’s a sharply satirical portrait of a new business generation operating without a moral compass.

One of Hollywood’s best young actors, Jesse Eisenberg (pictured right) has shown warmth and intelligence in Roger Dodger, The Squid and the Whale and Adventureland. As Mark Zuckerberg, he switches off the warmth but keeps the intelligence.

He is so chillingly arrogant that he becomes exhilarating in his self-belief. He persuades you that his coldness and detachment from conventional morality were central to Facebook’s success.

Much of the film takes place as Mark is being attacked in separate lawsuits, both of which lead to flashbacks from varying points of view. One suit is by identical twins Cameron and Tyler Winklevoss (muscular rowers who tower over our diminutive anti-hero and are played with an odious air of entitlement by Armie Hammer) who claim that Zuckerberg stole the idea for Facebook from them.

Screenwriter Aaron Sorkin (The West Wing) avoids taking sides, but shows why Zuckerberg resented the Winklevosses’ snobbery, and not unreasonably considered himself their creative superior. As he put it, “They came to me with an idea; I had a better one”.

The other lawsuit is brought by Eduardo Saverin (British actor Andrew Garfield, nuanced and touching). He’s Zuckerberg’s only friend and original business partner, suing for what he regards as his rightful share of Facebook – 600 million dollars.

Sorkin has obvious sympathy for the way Eduardo was frozen out, but also recognises that the company outgrew his naivety and needed the contacts of his rival, Napster founder Sean Parker, played by Justin Timberlake (pictured left) with an explosive mixture of confidence and paranoia, magnetism and sleaze.

Most movies have a moral centre, but this one has more of a moral tangent. Well played by Rooney Mara, who’s playing Lisbeth Salander in Fincher’s forthcoming remake of The Girl With The Dragon Tattoo, she’s an invented character called Erica, who appears to be an amalgamation of several Zuckerberg girl-friends. We meet her in the opening scene, where she becomes even more annoyed than we are by Mark’s fretting about social status, his arrogance and his lack of emotional empathy.

Later on, he makes some attempt to apologise, and she rounds on him for his misogyny, his thoughtlessness and his obsessiveness. At the end, the movie hints that she is the equivalent to Citizen Kane’s Rosebud, the unattainable object of Zuckerberg’s desire. It’s a rare concession to sentiment.

In most movies, Erica would redeem the leading figure, but here she’s condemned to be peripheral. This movie has, quite deliberately, an amoral centre. Zuckerberg doesn’t care much if he’s redeemed or not. What he minds about is his project.

The nearest thing Mark shows to love is in a restaurant when Parker reveals that he is on the same wavelength as Zuckerberg about the direction Facebook ought to take. There’s a meeting of minds, a near-sexual frisson, a touch of hero-worship in Zuckerberg’s eyes - and this is the moment when Eduardo first realises he is being left out in the cold.

Not everyone will respond to this very masculine movie. After all, it’s asking us to care what happens between a number of rich young American males fighting over percentages. There are few concessions to anyone too slow to follow the whip-smart dialogue. Not everyone is going to understand what’s happening, let alone be bothered about who wins.

But even Fincher and Sorkin remain detached from the struggle and its outcome. They’re fascinated by the characters, and especially by the way Zuckerberg himself is extraordinary, yet typical.

In a welcome return to form after the skilled but schmaltzy Benjamin Button, Fincher directs with the same hard-hitting panache he brought to Fight Club and Se7en. The technical wizardry that enables him to cast the same actor as identical twins is breathtaking because of its invisibility.

He is also a master at generating suspense and a variety of moods.

You get a feeling for the atmosphere of a dorm at Harvard where no one sleeps, a pitch to a New York businessman going horribly wrong, a rented house in California full of immature geeks. Without unnecessary flashiness, different scenes stylishly reflect Eduardo’s helplessness, Parker’s paranoia, Zuckerberg’s icy indifference to any opinion other than his own.

I was reminded of Budd Schulberg’s comic novel about an opportunist, What Makes Sammy Run? and F. Scott Fitzgerald’s classic parable about the rich, The Great Gatsby. Most of all, it’s reminiscent of Stephen Sondheim’s brilliant commercial failure, Merrily We Roll Along, a musical about a Richard Rodgers-like composer who sacrifices personal relationships in pursuit of worldly success.

This is not a film that bothers to dissect the allure and shortcomings of Facebook; it’s too busy showing us its vision of the characters involved. But the callous way the anti-hero uses the internet first to bully his former girl-friend and then to inquire if she will be his friend exposes a very interesting and significant dysfunctionality in the Facebook generation.

One thing’s for sure. See this movie, which manages the rare feat of being both entertaining and a cultural landmark, and you’ll never be able to hear the expression “Facebook friend” without mentally putting inverted commas around it.